Finite Group Databasebeta

← C13×#9991 #15696330

Subgroups — C13×#9991 #15696330

Order 3328.

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3195C211yesmaximal, characteristic
2C2×C13×#451C212yesmaximal
3C13×#1784C211yesmaximal, characteristic
4C13×#1472C212yesmaximal
5C13×#1298C211yesmaximal, characteristic
6C23×Q8×C13C2211yescharacteristic
7C22×C13×Q16—22no—
8C2×C13×C22⋊Q8C2212yes—
9C13×#483—22no—
10C13×#470—22no—
11C13×#451—22no—
12C13×#451—24no—
13C13×#451—24no—
14C2×C13×#103—22no—
15C2×C13×#101—22no—
16C13×#407C2211yescharacteristic
17C13×#407C2211yescharacteristic
18C2×C13×C22⋊C8C2212yes—
19C13×#324—24no—
20C22×Q8×C13—21no—
21C22×Q8×C13—22no—
22C22×Q8×C13—22no—
23C22×Q8×C13—44no—
24C22×Q8×C13D412yes—
25C22×Q8×C13D412yes—
26C23×C4×C13—21no—
27C23×C4×C13C2311yescharacteristic
28C2×C13×Q16—28no—
29C2×C13×Q16—22no—
30C2×C13×Q16—48no—
31C2×C13×M16—21no—
32C2×C13×M16D412yes—
33C22×C8×C13—22no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8—22no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4D412yes—
40C2×C13×C22⋊C4—22no—
41C13×#106—22no—
42C13×#103—28no—
43C13×#103—24no—
44C13×#101—44no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8D414yes—
49#9991C1311yesmaximal, characteristic, direct product factor, Sylow
50C24×C13#4111yescharacteristic
51C2×Q8×C13—24no—
52C2×Q8×C13—28no—
53C2×Q8×C13—24no—
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13—44no—
57C2×Q8×C13—44no—
58C2×Q8×C13—42no—
59C2×Q8×C13—44no—
60C2×Q8×C13—48no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—42no—
67C22×C4×C13—44no—
68C22×C4×C13—42no—
69C22×C4×C13C2×D412yes—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D412yes—
73C13×Q16—416no—
74C13×Q16—82no—
75C13×M16—42no—
76C13×M16—42no—
77C2×C8×C13—22no—
78C2×C8×C13—24no—
79C2×C8×C13—44no—
80C2×C8×C13—41no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87#3195C2×C1311yescharacteristic
88C2×#451C2×C1312yes—
89#1784C2×C1311yescharacteristic
90#1472C2×C1312yes—
91#1298C2×C1311yescharacteristic
92C23×C13—24no—
93C23×C13—41no—
94C23×C13#12111yescharacteristic
95C23×C13#12112yes—
96Q8×C13—28no—
97Q8×C13—44no—
98Q8×C13—44no—
99Q8×C13—44no—
100Q8×C13—44no—
101Q8×C13—44no—
102C2×C4×C13—24no—
103C2×C4×C13—22no—
104C2×C4×C13—24no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—48no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—44no—
113C2×C4×C13—82no—
114C2×C4×C13#12012yes—
115C2×C4×C13#12011yescharacteristic
116C2×C4×C13#12711yescharacteristic
117C8×C13—44no—
118C8×C13—42no—
119C8×C13—81no—
120C23×Q8C22×C1311yescharacteristic
121C22×Q16—22no—
122C2×C22⋊Q8C22×C1312yes—
123#483—22no—
124#470—22no—
125#451—22no—
126#451—24no—
127#451—24no—
128C2×#103—22no—
129C2×#101—22no—
130#407C22×C1311yescharacteristic
131#407C22×C1311yescharacteristic
132C2×C22⋊C8C22×C1312yes—
133#324—24no—
134C22×C13—22no—
135C22×C13—22no—
136C22×C13—22no—
137C22×C13—21no—
138C22×C13—44no—
139C22×C13#39211yescharacteristic
140C22×C13#47314yes—
141C4×C13—22no—
142C4×C13—21no—
143C4×C13—44no—
144C4×C13—82no—
145C4×C13—82no—
146C4×C13B(4,𝔽2)12yes—
147C22×Q8—21no—
148C22×Q8—22no—
149C22×Q8—22no—
150C22×Q8—44no—
151C22×Q8D4×C1312yes—
152C22×Q8D4×C1312yes—
153C23×C4—21no—
154C23×C4C23×C1311yescharacteristic
155C2×Q16—28no—
156C2×Q16—22no—
157C2×Q16—48no—
158C2×M16—21no—
159C2×M16D4×C1312yes—
160C22×C8—22no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4D4×C1312yes—
167C2×C22⋊C4—22no—
168#106—22no—
169#103—28no—
170#103—24no—
171#101—44no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8D4×C1314yes—
176C2×C13—24no—
177C2×C13—41no—
178C2×C13#202012yes—
179C2×C13#202111yescharacteristic
180C24C13×#4111yescharacteristic
181C2×Q8—24no—
182C2×Q8—28no—
183C2×Q8—24no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—44no—
187C2×Q8—44no—
188C2×Q8—42no—
189C2×Q8—44no—
190C2×Q8—48no—
191C2×Q8—41no—
192C2×Q8—41no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—42no—
197C22×C4—44no—
198C22×C4—42no—
199C22×C4C2×D4×C1312yes—
200C22×C4C2×D4×C1311yescharacteristic
201C22×C4C2×D4×C1311yescharacteristic
202C22×C4C2×D4×C1312yes—
203Q16—416no—
204Q16—82no—
205M16—42no—
206M16—42no—
207C2×C8—22no—
208C2×C8—24no—
209C2×C8—44no—
210C2×C8—41no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C13#999111yescharacteristic, direct product factor, Sylow
218C23—24no—
219C23—41no—
220C23C13×#12111yescharacteristic
221C23C13×#12112yes—
222Q8—28no—
223Q8—44no—
224Q8—44no—
225Q8—44no—
226Q8—44no—
227Q8—44no—
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—48no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—82no—
240C2×C4C13×#12012yes—
241C2×C4C13×#12011yescharacteristic
242C2×C4C13×#12711yescharacteristic
243C8—44no—
244C8—42no—
245C8—81no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—21no—
250C22—44no—
251C22C13×#39211yescharacteristic
252C22C13×#47314yes—
253C4—22no—
254C4—21no—
255C4—44no—
256C4—82no—
257C4—82no—
258C4C13×B(4,𝔽2)12yes—
259C2—24no—
260C2—41no—
261C2C13×#202012yes—
262C2C13×#202111yescharacteristic
subgroupG/H
center, socleC22×C13#392
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
49. #9991C13direct (N × H)
217. C13#9991direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#31952
C2×C13×#4512
C13×#17842
C13×#14722
C13×#12982
#999113